Call for a Coherent Math Curriculum

On February 6, 2003, the U.S. Department of Education
launched its new Mathematics and Science Initiative,
whose goals include to develop a major academic research base of what
boosts student learning in mathematics and science, further engage the
public, and enhance teacher knowledge. Papers and Power Point
presentations are available at
http://www.ed.gov/inits/mathscience/summit.html
Of particular interest were presentations by W. Schmidt of Michigan
State University, and G. Whitehurst, then Director of Institute of
Education Sciences:

Schmidt discussed the need for a coherent mathematics curriculum
and pointed out the lack of consistency among U.S. states regarding
when and how many concepts are introduced at grade levels in the
U.S. Readers will be interested in his Power Point slide #3 which
shows a "Coherent Curriculum in A+ Countries" for mathematics
(excellent visual listing mathematics curriculum strands and when
concepts are introduced) and then slides 4 and 5 regarding the
varied introduction of concepts in different states.

Whitehurst presented research on the effectiveness of practices
and policies in mathematics education with respect to tracking,
assessment, structured peer feedback, the Math Wars (constructivist
approaches to learning mathematics vs. traditional direct
instruction), the role of conceptual understanding, effectiveness of
constructivist curricula vs. skills-based curricula, and alignment
of the components of policy and practice. Readers short on time
should at least read his summary, "Putting It all Together." There
is an extensive reference list on research in mathematics education,
which was used to prepare the presentation.

In A Coherent Curriculum: The Case for Mathematics, William Schmidt,
Richard Houang, and Leland Cogan (2002) "define content standards and
curricula to be coherent if they are articulated over time as a sequence
of topics and performances that are logical and reflect, where
appropriate, the sequential and hierarchical nature of the disciplinary
content from which the subject matter derives" (p. 9). In looking at
the A+ composite for mathematics by topic and grade, data suggests three
tiers (p. 6):

Grades 1-4 includes emphasis on arithmetic, including common and
decimal fractions, rounding, and estimation;

Grades 5-6 are transitional, with continued emphasis on a few
arithmetic topics, but also an introduction to topics such as
percentages, negative numbers, integers and their properties,
proportional concepts and problems, two-dimensional coordinate
geometry, and geometric transformations;

Grades 7-8 consists of topics such as number theory (including
primes and factorization, exponents, roots, radicals, orders of
magnitude, and rational numbers and their properties), algebra
(including functions and slope), and geometry (including congruence
and similarity, and 3-dimensional geometry).

Continuity across all three tiers is provided by such continuing
topics as measurement units (grades 1-7), and equations and formulas
(grades 3-8).

HOT:
September 12, 2006: In response to the call for a more coherent
curriculum, the National Council of Teachers of Mathematics
released Curriculum Focal Points for Prekindergarten through Grade 8
Mathematics: A Quest for Coherence (NCTM, 2006a). In
its press release on September 12, 2006, NCTM indicated that
this document identifies three important topics for mathematics
at each grade level preK-8 and presents "a vision for the design
of the next generation of state curriculum standards and state
tests" (NCTM, 2006b, para. 3).

HOT: March 13, 2008: The National Mathematics Advisory
Panel, created by President George W. Bush in April 2006,
released the results of its study to the President and U.S.
Secretary of Education Margaret Spellings on the best use of
scientifically based research to advance the teaching and
learning of mathematics. The report,
Foundations for Success: Report of the National Mathematics
Advisory Panel, contains 45 findings and recommendations for
improving mathematics achievement for all U.S. students.
Its numerous topics include curricular content, learning
processes, teachers and teacher education, instructional
practices, instructional materials, assessments, and research
policies and mechanisms.

Of particular relevance was the development of a list of major
topics in school algebra (see p. 16) and the critical
foundations in K-8 math education for algebra: whole numbers,
fractions (including decimals, percents, and negative
fractions), and aspects of geometry and measurement (see p. 17).
"School algebra is a term chosen to encompass the full body of
algebraic material that the Panel expects to be covered through
high school, regardless of its organization into courses and
levels. The Panel expects students to be able to proceed
successfully at least through the content of Algebra II"
(Executive Summary, p. xvii).

HOT: June 1, 2009:
Common Core State Standards Initiative: In its June 1
press release, the
National Governors Association Center for Best Practices and the Council
of Chief State School Officers (2009) announced that 49 states
and territories joined the Common Core State Standards Initiative.
This initiative is "a state-led process to develop a common core of state standards in
English-language arts and mathematics for grades K-12. These standards
will be research and evidence-based, internationally benchmarked,
aligned with college and work expectations and include rigorous content
and skills" (para. 3). For updates and additional news on these
standards, see
http://www.corestandards.org/

HOT: October 6, 2009:
As a follow-up to its 2006 Curriculum Focal Points, NCTM releasedFocus in High School Mathematics: Reasoning and
Sense Making, a "conceptual framework to guide the development of future
publications and tools related to 9–12 mathematics curriculum and instruction."
It highlights reasoning opportunities in numbers and measurements, algebraic
symbols, functions, geometry, statistics and probability (NCTM,
2009a). In its press release NCTM stated that this book "suggests practical changes
to the high school mathematics curriculum to refocus learning on reasoning and sense
making. This shift is not a minor refinement but constitutes a substantial rethinking of the
high school math curriculum" (NCTM, 2009b, para. 1). Reasoning habits
are organized into four broad categories: analyzing a problem, implementing a
strategy, seeking and using connections, and reflecting on a solution (NCTM,
2009a, FAQs, p. 4).

HOT: September 7, 2011: The
Mathematics
Common Core Coalition was formed to "ensure the successful
communication, interpretation, implementation, and assessment of the
Common Core State Standards" (Mission statement section). There
are eight member organizations providing their expertise and advise on
issues.

HOT: May 2012:
From an announcement by Achieve.org,
Common Core Math Standards Implementation Can Lead to Improved Student
Achievement, we learn that "Dr. William Schmidt released key
conclusions from his research detailing how the Common Core State
Standards (CCSS) for mathematics can potentially improve the performance
of U.S. students if implemented appropriately" (para. 1). Dr. Schmidt's work
was entitled: Common Core State Standards Math: The Relationship
Between High Standards, Systemic Implementation and Student Achievement.
"Unlike previous research, Schmidt analyzed the link between states with
standards that were similar to the CCSS and their NAEP [National
Assessment of Educational Progress] math scores. He used cut scores
aligned to NAEP as a proxy to determine if states were serious about
high expectations and implementation of standards. The preliminary
results showed states with standards in line with CCSS combined with
higher cut scores also had higher NAEP scores" (para. 7). A
PowerPoint
Presentation and video are available related to this research.

Read The
Promise of the Common Core by Al Cuoco (2014, January 15) at the
Habits of Mind Blog from the Education Development Center's Mathematical
Practice Institute.

Initiatives

Achieve is an advocate for Math Works: "Math
Works materials—ranging from fact sheets, PowerPoint presentations,
brochures and others—are resources for policymakers, advocates, educators,
parents and students alike that highlight the connection between higher-level
mathematics course-taking and college access and success, workplace and career
readiness, and personal and U.S. competitiveness" (About Math Works section).

In other work of Achieve, "To help states work toward the rigorous high
school math goals set forth by the American Diploma Project, Achieve has created
a set of expectations that comprise the mathematical skills and knowledge that
students will need to learn from kindergarten through 8th grade."
Foundations for
Success, published in 2002, contains math expectations for the end of grade 8, which
incorporates fundamentals that students are learning in top-performing countries. It
contains illustrative problems and sample solutions that focus on
concepts, which are difficult to teach and need clarification. Foundations for Success
also notes topics for grades 1-5, and 9-11 in the appendices.

Achieve's
American Diploma Project Assessment Consortium has posted practice tests and
released test items from the recent end of course exams for Algebra I and
Algebra II, respectively. Achieve also has documents to help states, districts, and others to
understand and then implement the Common Core State Standards.

California Free Digital Textbook Initiative
provides a list of open-source books approved for use in
California. There are several publishers. Among math texts
meeting California standards are algebra II, calculus, trigonometry, and
geometry.

Common Core State Standards Initiative,
as described at the web site, "is a joint effort by the National Governors Association
Center for Best Practices (NGA Center) and the Council of Chief State
School Officers (CCSSO) in partnership with Achieve, ACT and the College
Board. Governors and state commissioners of education from across the
country committed to joining a state-led process to develop a common
core of state standards in English-language arts and mathematics for
grades K-12." These standards are research and evidence-based,
internationally benchmarked, aligned with college and work expectations
and include rigorous content and skills. Read the full set of standards
for K-12 mathematics at
http://www.corestandards.org/Math, which were
released in their final form on June 2, 2010.

Note: Educators might appreciate the
Common Core
Video Series posted at EngageNY.org. Although meant for New York
educators, this 15-part series will provide valuable insights for all who
have adopted the Common Core State Standards. Educators and
administrators will "learn step-by-step how to implement the Common Core for
ELA/Literacy and Math in their schools and classrooms. You’ll also gain a
deeper understanding of the rationale behind the Common Core and what it
will mean for students ..." (EngageNY, Common Core Video Series, August 1,
2011, para. 1). Also see: Education
Northwest Common Core State Standards Mathematics Resources.

EdReports.org is an
independent, non-profit launched in winter 2014. Its goal is to provide "
free web-based reviews of instructional materials series focusing on alignment to
the Common Core and other indicators of high quality as recommended by
educators, including usability, teacher support and differentiation. These
Consumer Reports-style reviews will highlight those instructional materials
that are aligned to the higher standards states have adopted so that
teachers, principals and district and state officials charged with
purchasing materials can make more informed choices" (Website description
section).

Idaho Math Initiative
from the Idaho Department of Education "will focus on improving math education in
all grades to ensure every student is prepared for higher levels of math
in the middle grades, high school, post-secondary, and work-force
setting." The Idaho Math Initiative will offer professional
development for teachers, assessment tools for all grades and
research-based intervention programs for students.

Illustrative Mathematics Project is a work in progress to produce illustrative tasks of the
Common Core State Standards for Mathematics. Sections address
illustrations for the K-8 and High School standards. The project is an
initiative of the Institute for Mathematics & Education and the Bill &
Melinda Gates Foundation.

IMAGES: Improving Measurement and Geometry in Elementary Schools
is an initiative of the Pennsylvania State Team of the Mid-Atlantic
Eisenhower Consortium for Mathematics and Science Education at Research
for Better Schools. You'll information and
resources that are designed to help teachers develop a deeper
understanding of geometry and measurement concepts and to assist in
designing meaningful instruction for elementary students.

K-12 OER Collaborative is creating comprehensive, high-quality, open
educational resources (OER) supporting Mathematics and English Language Arts
aligned with state standards. "This project is a state-led collaborative, with support provided by many of the
leading non-profits in OER and education" (FAQ section).

Mathematics Common Core Coalition was formed to "ensure the successful
communication, interpretation, implementation, and assessment of the
Common Core State Standards" (Mission statement section). There
are eight member organizations providing their expertise and advise on issues.

Mid-Continent Comprehensive Center (MC3)
has a list of STEM initiatives by state. The center is "one of a national
network of 21 federally funded centers designed to assist state education
agencies (SEAs) increase capacity to provide sustained support to districts and
schools as they implement the Elementary and Secondary Education Act" (About MC3
section).

National Math and Science Initiative:
This initiative's
mission is to improve student performance in the critical subjects of science,
technology, engineering and math (STEM). It also includes Uteach (http://www.uteach.utexas.edu/)
to recruit and prepare more math, science and computer science majors
for careers in secondary teaching and Advanced Placement (AP) Strategies
(http://www.apstrategies.org/).
You'll find free lessons and Common Core Open Resources within its
Resource section.

National Science Foundation Standards-based Curriculum
Projects are located at four centers:

The ARC Center:
http://www.comap.com/elementary/projects/arc/ is a
collaboration between the Consortium for Mathematics and Its
Applications (COMAP) and the three National Science Foundation
supported elementary mathematics curriculum projects:

COMPASS (Curricular Options in Mathematics Programs
for all Secondary Students):
http://fuse.ithaca.edu/compass-points-8484/ and its satellite sites provides information and assistance for
implementation of five secondary curriculum projects that support
NCTM standards:

Integrated Mathematics: A Modeling Approach
Using Technology: Systemic Initiative for Montana Mathematics
and Science Project (SIMMS) (9-12):
http://www.montana.edu/wwwsimms/SIMMS Integrated Mathematics
curriculum is a complete NCTM Standards-based mathematics
curriculum for all students which incorporates a modeling
approach using technology and involves real world contexts.
The SIMMS Project from the University of Montana at Bozeman
has been discussed in NCTM's Mathematics Teacher and ENC's Focus
Magazine, and is one of the NSF funded projects.

Project 2061 is the long-term initiative of the American Association
for the Advancement of Science to reform K-12 science, mathematics, and
technology education nationwide. School districts will be most
interested in the evaluation of middle school mathematics and science
textbooks from leading publishers, which is available online. The
analysis is based on project standards and reveals the best texts for
learning mathematics. Read Benchmarks Online and associated
research, and Blueprints for Reform, an examination of 12 aspects of a
K-12 system. These aspects are grouped into three parts:
Foundation, School Context, and Support Structure. Join the
dialogue.

Success for All Foundation (SFAF) is a comprehensive school restructuring program for elementary
schools in reading, writing, mathematics, and social studies. It's
mission is to raise achievement of students in those areas. The
curriculum can be found in about 1800 elementary schools in 48 states.
A middle school pilot project is also underway.

STEMconnector.org
promotes itself as a "one-stop shop for who's doing what in Science,
Technology, Engineering, and Math." It is a "nationwide
collaboration of companies, nonprofit associations and professional
societies, STEM-related research & policy organizations, and academic
institutions concerned about the plight of STEM education in
the United States" (About section). You'll also find state
information, STEM projects and competitions, sections devoted to diversity,
women/girls, national labs, and much more.

TERC
is a not-for-profit education research and development organization in
Cambridge (MA), whose mission is to improve mathematics, science, and
technology teaching and learning. Work includes "research,
curriculum and technology development, and implementation support in the
form of professional development and assistance to districts and schools."

National Council of Teachers of Mathematics (2009b,
October 6). NCTM Releases new landmark publication: Focus in
High School Mathematics: Reasoning and Sense Making. Reston,
VA: NCTM News Release. Retrieved from
http://www.nctm.org/news/content.aspx?id=23876